Try upgrading it to 3.40 OE-A.
Then make a folder on the root of the PSP called ISO.
Put your DL games in the ISO folder.
Make sure you have RAR file.
Also make sure that the game is either ISO or CSO.
Heres the forum link to the 3.40 OE-A.http://forums.afterdawn.com/thread_view.cfm/500493

the problem your facing is due to the games requiring a higher firmware then 3.10 so that's why they wont run, could be 3.11 or 3.3 or whatever, but just upgrade from where you are now to 3.40OEA and that little inconvenience should be fixed.